Both the European Central Bank and the Fed, which holds a policy meeting Tuesday and Wednesday, have cited similar reasons for their policy shift - the threat of a softening global economy if Trump and the Chinese don't reach agreement on trade.
Those comments, which economists said implied rate cuts before the end of the year and a return to the purchase of eurozone government bonds, caused the euro to fall by 0.3pc against the dollar to $1.1182, and pushed yields on eurozone bonds, which were already at record lows, even lower.
Trump tweeted in fury after European Central Bank President Mario Draghi signaled his bank could cut interest rates or expand its bond-buying program, which promptly boosted both the European stock market and the Euro. Fed Chair Jay Powell has said that the Fed is prepared to respond if it decides the U.S.
Mr Trump has repeatedly criticized the Fed and pressured Powell to cut rates, and on Tuesday lashed out at Mr Draghi's statements, saying an European Central Bank cut would "unfairly" harm USA goods competing with a cheaper euro. They have been getting away with this for years, along with China and others.
Draghi's speech sank the euro and drove major euro zone bond yields back below zero, slashing effective market borrowing costs, giving a boost to companies anxious by sagging growth and driving the pan-European STOXX 600 index nearly 2 per cent higher.
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His call to bring back the death penalty didn't include minors, he explained, but they should be absolved of punishment, either. Trump responded, "You have people on both sides of that".
The dollar index, which measures the greenback against a basket of currencies, rose 0.06 per cent, with the euro down 0.18 per cent to US$1.1197 (S$1.5304).
Draghi, meanwhile, said if the economic situation deteriorates in the coming months then more stimulus measures will be needed.
Trump also said he would have an extended meeting with Chinese President Xi Jinping at the G-20 summit later this month, as the world's two largest economies rekindle trade talks. Trump wrote on Twitter minutes later.
President Trump has complained about the Federal Reserve's monetary tightening, which he said is making it more hard to accelerate economic growth.
The dollar traded near two-week highs against the euro on Wednesday as investors waited to see whether the U.S. Federal Reserve would sound as dovish on future interest rate cuts and stimulus as the European Central Bank.
Europe has been grappling with a sluggish economy beset by low inflation.